Peter Gärdenfors is an Emeritus Professor at Lund University at the Department of Philosophy. His work is at the intersection of philosophy, cognitive, psychology, and linguistics. In this conversation, we discuss his book Conceptual spaces and many of the topics discussed therein (convexity, prototypes, metrics), whether the theory is falsifiable, how it can explain aspects of semantics and of how children learn, and much more.
BJKS Podcast is a podcast about neuroscience, psychology, and anything vaguely related, hosted by Benjamin James Kuper-Smith.
Support the show: https://geni.us/bjks-patreon
Timestamps
0:00:04: Where is the neuroscience (especially about spatial navigation) in Conceptual Spaces?
0:04:54: What are conceptual spaces?
0:14:53: How Peter went from decision theory to knowledge representation
0:20:25: Dimensions and metrics in conceptual spaces
0:35:29: Is the theory of conceptual spaces falsifiable?
0:38:41: Conceptual spaces of semantics
0:51:54: 3 levels of representation across evolution
0:55:41: The future of conceptual spaces
1:01:09: Something Peter wishes he'd learned sooner
1:04:31: A paper or book Peter thinks more people should read
Podcast links
Peter's links
Ben's links
References
Bellmund, Gärdenfors, Moser & Doeller (2018). Navigating cognition: Spatial codes for human thinking. Science.
Gardenfors (2004). Conceptual spaces: The geometry of thought. MIT press.
Gardenfors (2014). The geometry of meaning: Semantics based on conceptual spaces. MIT press.
Marr (1982). Vision: A computational investigation into the human representation and processing of visual information. MIT press.
Zwarts & Gärdenfors (2016). Locative and directional prepositions in conceptual spaces: The role of polar convexity. Journal of Logic, Language and Information.
First episode of our discussion of Conceptual Spaces as part of this podcast's book club series: https://geni.us/bjks-concept-space-1
Peter Gärdenfors is an Emeritus Professor at Lund University at the Department of Philosophy. His work is at the intersection of philosophy, cognitive, psychology, and linguistics. In this conversation, we discuss his book Conceptual spaces and many of the topics discussed therein (convexity, prototypes, metrics), whether the theory is falsifiable, how it can explain aspects of semantics and of how children learn, and much more.
BJKS Podcast is a podcast about neuroscience, psychology, and anything vaguely related, hosted by Benjamin James Kuper-Smith.
Support the show: https://geni.us/bjks-patreon
Timestamps
0:00:04: Where is the neuroscience (especially about spatial navigation) in Conceptual Spaces?
0:04:54: What are conceptual spaces?
0:14:53: How Peter went from decision theory to knowledge representation
0:20:25: Dimensions and metrics in conceptual spaces
0:35:29: Is the theory of conceptual spaces falsifiable?
0:38:41: Conceptual spaces of semantics
0:51:54: 3 levels of representation across evolution
0:55:41: The future of conceptual spaces
1:01:09: Something Peter wishes he'd learned sooner
1:04:31: A paper or book Peter thinks more people should read
Podcast links
Peter's links
Ben's links
References
Bellmund, Gärdenfors, Moser & Doeller (2018). Navigating cognition: Spatial codes for human thinking. Science.
Gardenfors (2004). Conceptual spaces: The geometry of thought. MIT press.
Gardenfors (2014). The geometry of meaning: Semantics based on conceptual spaces. MIT press.
Marr (1982). Vision: A computational investigation into the human representation and processing of visual information. MIT press.
Zwarts & Gärdenfors (2016). Locative and directional prepositions in conceptual spaces: The role of polar convexity. Journal of Logic, Language and Information.
First episode of our discussion of Conceptual Spaces as part of this podcast's book club series: https://geni.us/bjks-concept-space-1
[This is an automated transcript that contains many errors]
Benjamin James Kuper-Smith: [00:00:00] Yeah, I mean, so I guess we'll be talking mainly today about, uh, conceptual spaces and your book with the same title, the Geometry of Thought as a subtitle. Uh, so for anyone, uh, listening to the podcast who thinks that might sound familiar, it's because Kuan and Iles is a fellow PhD student in our lab. We discussed this book already in a few parts.
Uh, we kind of, uh, it sounded very interesting, so went through it in several steps. So yes, this is the same book, uh, and now I'm talking to the author, which is very exciting. Yeah, I think I'd like to kind of just go, not through the book, but like discuss it, uh, quite broadly on the topics, um, that you discussed there.
And I thought, I really like the way you start in the book. So you do discuss kind of the two goals of cognitive sciences and kind of how conceptual spaces and your book fits into that. Um, could you maybe, could we maybe start.
Peter Gardenfors: Yeah, I, I think of myself as a cognitive scientist. So that's where the book should be located. I mean, I have a background mainly in, in mathematics and philosophy. I've studied some linguistics. Uh, I've dabbled in psychology, [00:01:00] uh, and, uh, I don't know very much about neuroscience, but I have some inklings on, on what's going on.
So it's, it's a book basically written for cognitive scientists, maybe a little bit for philosophers who are interested in, in the knowledge, representation problems, maybe a little bit for computer scientists who want to know something about how we could possibly represent the information, not in the symbolic, uh, type of, uh, of ways.
So, yeah, I hope that gives a description of what I think of my, as my audience.
Benjamin James Kuper-Smith: Yeah. Yeah. And, um, what, yeah, maybe, I mean, I thought I'll do this later, but maybe I'll just switch to it right now. I mean, you had this, this very nice sentence in the, in the beginning of your book. Uh, I think I. Read it out briefly because it kind of, I think it's a very nice metaphor. Uh, you said, while writing this text, I felt like a centor standing on four legs and waving two hands.
The four legs are supported by four disciplines, philosophy, computer science, psychology, and linguistics. And there's a tale of neuroscience since these disciplines put in [00:02:00] different directions, in particular when it comes to methodological questions, that's considerable risk that my cento has ended up in a four-legged split.
And, uh, first of all, I just very, like, I very much like that image. Um,
Peter Gardenfors: totally forgotten. Not quote.
Benjamin James Kuper-Smith: yeah. But, um, the, the, the thing I wanted to ask, which is basically the, the funny thing, kind of when, when I discussed this book with Koon, is that both of us come more from the neuroscience side and we very much, uh, I'm very, we're very much interested in special navigations and grid sales and all these kind of things, and I found out about.
By reading the review paper where your co-author, uh, in science, uh, with Yaba as first author. And so I always, I just assumed like, oh, cool, here's someone who's already written about all these things, uh, from a philosophical perspective. And so I was really surprised then to see that, you know, neuroscience isn't one of the four legs of this book.
Um, and then in particular that you basically cite none of the special navigation literature, [00:03:00] which to me was I, I thought it was like, so, uh, I thought it was gonna be central to the book.
Peter Gardenfors: Yeah, yeah. No, I mean, this book was written, you know, basically 25 years ago, pub published in, in 2000. And at that time I had very little knowledge about spatial navigation. Um, a lot of the experiments, I mean, Moses's work was, was hardly there. And, uh, that was o okay, uh, O'Keefe's work and so on. I knew a li both basically, but I was just too afraid to write too much about the, uh, uh, about the, uh, neuroscience in the book because I, I wrote a little bit about topographic mappings and that, that's about it, uh, that I, that put in the book.
So it's, it's more written for computer scientists and psychologists and, and philosophers. I said, as I said,
Benjamin James Kuper-Smith: Yeah, yeah, yeah. You're, and you're obviously right that this was before the discovery of grid cells and all this kind of thing, and the mos, I guess, had kind of just gotten going in that sense. But, uh, yeah, so it's, it's basically, um, yeah. I guess what I found fascinating is it [00:04:00] seems there were like these.
To parallel literatures almost, um, that develop very similarly to kind of suggesting that conceptual space, something very useful without, I guess now they're starting in part Yeah, they're, they're starting to overlap, but I guess not before that.
Peter Gardenfors: I mean, it was, it was Jacob Pelman who con contacted me and said he found my, my theory is interesting because he thought that it could be used to explain what the Hippo Compass is doing when it's not doing spatial navigation. Now that is, it's navigating in other spaces, I mean, in other conceptual, uh, spaces.
So, so he, we, we joined efforts and, and in, in writing this, well, he did most of the job. But anyway, I, I, I helped him in, in getting this, uh, error concept of spaces right and so on.
Benjamin James Kuper-Smith: Yeah. And uh, they're, I've talked to Yakob on the podcast, so there's an entire episode about, uh, half an episode about that paper. Um, I guess we've already mentioned space and that stuff, but what are they, we haven't really talked about what, what they are, what does a conceptual space and what does it do?
Peter Gardenfors: It's a way of using space. [00:05:00] I mean, I, I take this mathematical concept, uh, quite literally. I mean, it's a set of dimensions with, with a metric, and that I used to represent information in different domains. And so my paradigm example is color space. But you can have, you can have size, you can have temperature, you can have weight, you can have sound, uh, or maybe some social structures can be represented in, in various spatial structures.
And, uh, in the, in the book, I tried to develop this idea, uh, to say little bit about how you can do it mathematically, leaving lots of things open, uh, but also how that, how that can be used to understand various aspects of concept learning and, and, uh, uh, inductive reasoning and, uh, and, uh, semantic questions.
Since I wrote the book, I have continued on in the era semantics quite a lot.
Benjamin James Kuper-Smith: Yeah, I think I'll ask a few more detailed question about semantics, uh, later on, uh, because that's a topic I know basically nothing about. Um, [00:06:00] so I guess that's where I can learn the most. But, uh, yes. I mean, what do, um, or maybe you, you talked about two different, um, you talk about these three levels of representation, uh, symbolic, um, asso, associa, I keep forgetting how it's pronounce association.
Peter Gardenfors: Neural. Neural networks,
Benjamin James Kuper-Smith: yeah, exactly. And you kind of place conceptual spaces between them as a, as a bridge, as you call it. Um, can you maybe elaborate a little bit on that? Kind of what's the. Um, why kind of, if we already have these other two levels of representation, why do we need conceptual spaces and how does it kind of bridge them?
Peter Gardenfors: And I was, I was brought up in philosophy department using logical symbolism, and I, and I learned to program using symbols. So I was, my background was in, in doing, uh, knowledge representations, in terms of symbols, uh, you know, logical formulas or computer programs. Uh, but then I started studying ai and I, I realized there were lots of problems with, with, uh, [00:07:00] using these symbolic representations.
And, um, at the time, the neural networks were, were being developed and they solved certain problems. They can learn to recognize patterns, they can learn to circumvent the symbolic constraints. Um, I mean, you have to, don't have to define them. And, uh, at the beginning and, and, and so on, they can learn very basic things.
But the drawback of neural networks is, Uh, first of all, you don't know exactly what they're learning. Secondly, they're learning very slowly. Uh, you need a lots of training, lots of examples. You have to feed them lots of data in, in order for them to pick up some reasonable pattern. And I knew a little bit about how children learn new words and learn, learn new concepts, and it goes very quickly.
And the question is, how can we learn things so quickly? I mean, if, if, if the world, uh, needs to have some structure. So then I came up with this idea that if we sort up the world in, in some kind of geometrical structures where we have dimensions and spaces and so on, [00:08:00] then it's quite easy to explain how, how, uh, learning goes so quickly.
And that why, why we only need a couple of examples of the meaning of a word to, in order to understand it. We don't need to train thousands of times as the neural network does. So it, it was a way of trying to. Amplify the way of, um, uh, representing knowledge. Uh, and I put it in between because that's a question of le level of granularity.
I mean, they're given the conceptual spaces, you can identify word meanings as readings and the spaces, and you can learn, you can train neuro networks to generate those radis. So from a much lower, lower and fine, more fine-grained, uh, uh, levels. So in terms of, well, basically the gra granularity of representation, uh, concept of spaces come in between the symbolic level and the uh, uh, neural network level.
Benjamin James Kuper-Smith: One question I had whilst I was thinking about this is I was almost really surprised [00:09:00] that the conceptual level hadn't been described first. Um, and I kind of had this question like, why it took so long for someone to propose this, because when I, I just thought back about, because basically, you know, it's, it's, you know, you, I guess you just say we, we sort our world or not be sorted, but like we describe our world by different quality dimensions.
And we'll get a bit too into a bit more data of what that means later. I mean, that's basically what you do when you learn mathematics in, in high school when you're, you know, 10, 12 years old or whatever. Right. That, that's basically what you do. You learn, oh, this can, there can be a dimension and then you can plot it on a graph and et cetera.
Right? So I was kind of really surprised that this hadn't already happened like 300 years ago, basically. Um, yeah.
Peter Gardenfors: I mean, the, the history behind it is that in, in philosophy, logic was so dominant. I mean, the, the symbolic representations that was dominant as, as a way of describing reasoning and as representing knowledge. Everybody thought that we could catch all, all knowledge there is in, in, in logical formulas. And then in, in computer science, it was the same thing.
We had this [00:10:00] symbolic, uh, languages before there were neural network. The psychologists were doing things with dementia, so I, I borrowed some ideas from them. There are people, uh, like Shepherd and Osofsky who are, who are, have been working with, with spatial representations. But what I added to that was little bit more focused on the geometry.
So, um, I, I have one of the central notions in, in my book is that of dividing a space into readings and saying that for a natural concept, uh, the, the reading should be convicts. And this idea of convexity haven't found in any other psychologist. And for me, that has given a lot of mileage in terms of, uh, explanatory power.
Benjamin James Kuper-Smith: Okay. So what is convexity? Maybe that's something, uh, some, some one specific term I do need to ask about. What exactly does that mean?
Peter Gardenfors: Means that if one, if two points X and Y are both in the set, in, in a, in, in a set, then anything in between is also in the set. So [00:11:00] if you call one color shade for by red, the term red, and another color shade by the term red, any shade in between will also be called red. That's the, uh, the, the official definition of, of complexity.
It relies on the notion of between us. But if you have a space you can typically talk about between us.
Benjamin James Kuper-Smith: Mm-hmm. And how, how does convexity exactly. Help help us? Like what? Yeah.
Peter Gardenfors: Um, there are many reasons why Coex City helps us. Maybe the most important one is it's easy to learn because if you have learned a couple of examples of what is meant by, uh, red is not a good, good example by, um, but by, um, animal, uh, you've seen a couple of examples of, of a peculiar animal. And then you know that anything that is similar to anything that is in between.
I mean, this is kind of principle for generalization of observations you've already had. So if, if you have complexity, you can generalize the new instances. Um, so that helps explain why learning goes so quickly.
Benjamin James Kuper-Smith: So [00:12:00] basically as soon as you've acquired a few examples, you can infer whether something belongs to this category or.
Peter Gardenfors: And it also fits very nicely with what's called prototype theory in, in, uh, psychology. I mean, people say that we can't define concerts by necessary and sufficient conditions. That's what philosophers wants to do. But, um, we, we rather have prototype. There's a prototypical bird, there's a typical fruit that there's a typical piece of furniture and, and, and, and so on.
And once you've learned the prototype, then you can generalize. I mean, if you, if there, if you want to know whether something is an orange or an apple, then you, you check whether it's more similar to an orange than to an apple, and then you decide it must be an orange because it's more similar to you talk about distances in the space here.
So, um, and you and prototypes then are, are the centers of these convex radiants too. That's, uh, another connection here to con.
Benjamin James Kuper-Smith: Yeah, I really liked the prototypes. I mean, we can maybe use the example that you, um, use [00:13:00] in the, in the, in the science review with Yaman, because I think that's a very nice, uh, example where you have. Basically your two axes are the horsepower of a car, and the other axis is the weight of a car. And so, um, basically if you have these two ax axis, you can map all sorts of different cars.
So if you have a very heavy, very powerful car, it's, I mean, car in the loose sense here, it's, it's probably a lottery or truck or something like that. If you have a very powerful, very light car, it might be something like a Formula one car, something like that. And then you can really find this and, yeah.
Maybe can you just elaborate a little bit on that? Because I really, I thought, I mean, it's, it's slightly harder to describe when you see it in front of you, it's much more obvious.
Peter Gardenfors: That, that's a kind of toy example. Uh, because two dimensions for cars are not sufficient, but you can get rough sorting of, of certain, and maybe maybe the size or the power is not, maybe it's the shape of the car or something like that. That's, um, that goes, um, uh, into the central, uh, part of what is meant by a car or a truck.
And it's known that when children [00:14:00] learn words for new objects, new categories, they are very much biased towards shape. So the things are similar and shaped. They sort them by shape and then they learn that maybe some other aspects like sound or living behavior or something like that is more important for the categorization.
But if you sort things by shape, you do quite well and you can learn a lot of words by just looking at the shapes.
Benjamin James Kuper-Smith: Yeah. It's a fair point. I guess shape is the, it's probably the, the dimension that gives you like the, the most bang for your buck when you want to differentiate different kinds of
Peter Gardenfors: And And kids attuned to that, to that economy. Conceptually economy, we can call it.
Benjamin James Kuper-Smith: Yeah, exactly. And only once you become a bit older, you really need all these like, details that don't really matter that much. Um, yeah, maybe to, to take a little bit of a, of a step back. I'm kind of, I'm always curious like about how people got into the research that they, that they're doing. Um, [00:15:00] and I'm, in your case, I'm particularly interested because I looked at your early publications and it looked like it was more kind of, I mean, some of the stuff looked like stuff I read from, from my direct research, which it looks more like game theory, a bit of like fairness and all these kind of things.
And then that kind of gradually peters out kind of until by the nineties it seems like you're not really doing that much anymore. So I'm curious, like, how do you, it it seemed quite different. Um, and yeah. How did you end?
Peter Gardenfors: I, I wrote my PhD thesis on decision making and that's why the game theory comes in and, and stuff like that. But I've always been interested in knowledge, representation. I mean, I, I, I was educated as a program. I did some AI programs in, in Lisp during my, my Bachelor work and so on, and I got interested in how, how can we solve new problems with, uh, using AI and.
In philosophy of science, one of the major problems is, uh, the problem of induction. How can we go for observations of that certain, uh, ravens are, are [00:16:00] black to a generalization that all ravens are black, what do we need? And so on. And there are famous paradoxes in induction. So Carl Hempel has said that, okay, if we observe a, a raven, that that is black, that supports for the, for the, um, generalization that all ravens are black.
But he says that if we observe a, a, a, a brown shield, that is not a raven, then they, that that's also support because logically they are, they that supports for the, for the, uh, generalization that every non-black thing is non raven. And, uh, logically these are, these are equivalents and peop people in the, uh, logical traditions have been arguing for how this should be solved.
So I got. My question was how can we determine whether a concept is natural? So non-black is not very natural or non raven is definitely not a natural concept. Induction concerns, um, relations between natural concepts.
Benjamin James Kuper-Smith: would you be natural?
Peter Gardenfors: Well, [00:17:00] something that we can, that we can do generalizations about. Uh, another famous, uh, paradox is Goodman Paradox.
And he says that we can say that something is grew if it's GLE Green before 2025 and blew after 2025. So all the evidence we have says that all, all emeralds, they're not only green, but they're also grew, uh, and we don't expect them to change color when 2025 comes. So being grew is not a natural pre predicate, but green is a natural predicate.
How do we make a distinction? And that's why I came up with this idea that if we look at a geometric representation, we can say that the natural, uh, concepts, they are the convicts ones and, uh, some, some, uh, of these non raven will not be convicts, radient. And, and, uh, I have argued in the book that grew, it's not the convicts radian either.
So, um, if we want to have some kind of explanation of why we generalize from certain concepts and not [00:18:00] matters, then I think the geometry would play well. So that was actually my starting point. But then I began reading about, uh, how children learn concepts and so on. I found more and more support for this idea and, uh, that convexity could be a good idea to, uh, define what is a natural concept, that concept that we have words for, so to speak.
So that's totally de devoted from neuroscience.
Benjamin James Kuper-Smith: Yeah, yeah, yeah. No, but that's, that's kind of, you know, uh, why I find this fascinating. I mean, one of my last episodes I published was, was with Daniella Shila, and one thing we talked about there is that sheik comes. So from the, if you're from neuroscience, there's usually these two perspectives. One is of the hippocampus, one is memory.
Um, you know, you have procedural memory or episodic memory for, you know, events in your life. And there's the, you know, Hm. The amnesic patient is the most fun example there. And then there's this other entire literature, this other approach, which is coming more from, you know, the special navigation that you're.
Play [00:19:00] sales on hippocampus and that kind of stuff. And it's really interesting to me that you have a, basically a third approach to this whole.
Peter Gardenfors: Well, well, yes and no because we, we couldn't say, I mean, this is the idea in the paper with Belman that, uh, the Hippo Compass is not doing only special representations of ordinary space, but doing special representations of all other kinds of things. So we have codes for colors and for shapes and, and whatnot.
And, and, uh, they are represented differently in the, um, in the play cells. But the, the idea is that the grid cells function as a kind of universal, universal coordinate. So that that's, uh, that's how we, how we can do these, uh, spatial, uh, representations. Then how this really connects to episodic memory is another step, but we can at least say something about how the different concepts are coded that we, that we, or memories sometimes are more or less similar to the real things and so on.
Yeah.
Benjamin James Kuper-Smith: Yeah. Yeah. Sorry. I meant, I forgot to say like that the, that all of this points towards what in [00:20:00] neuroscience we think of as these well conceptual spaces to use your term now. Um, that, that, yeah, exactly. The spatial navigation system. It might just be a coincidence that we happen to find spatial navigation rather versus navigation in other kinds of spaces, or kind of physical spatial navigation rather than any other kind of conceptual.
Yeah, I mean, I thought maybe we could talk a little bit more about, um, to kind of make this a little bit more concrete about the different dimensions. I mean, since you mentioned color already and you use it, you know, frequently in the book as an example, and I maybe one thing I, I find it interesting example because in a way color seems like it might not apply that well to your theory in, in some ways because for color we have this really weird thing that we perceive it kind of as a circle rather than as a line that goes from A to B, even though the electromagnetic spectrum does go from A to B.
And I mean, one thing I already mentioned in our book discussion is that, um, this is ex, when you [00:21:00] edit photos, uh, on software, you have this color wheel. It, it looks exactly like the, the image you have in your book. Um, I'm just cur do you, uh, one just general question I had, are there other kind of dimensions that don't really match the.
The, the representation, the way it actually is in reality, so to speak. So like, you know, with color, like why, for example is sound linear or more or less linear. At least it goes from A to B, but color is a circle. Like why doesn't sound like suddenly when you have very high notes, suddenly it becomes a low note.
Like are there other examples like that?
Peter Gardenfors: Um, good question. First of all, I should say that I picked the color space as a good, an example because it's well researched and we know the distances in the space. I mean, people, the psychologists have been asking people to compare color chips and ask how similar are they? And so on. And based on various techniques like multidimensional scaling, they have established that we have this kind of three-dimensional room, [00:22:00] uh, three-dimensional perception of colors.
And if you do that with, with cows, you only get a two dimensional base because they can't make the red, green, uh, discrimination. And if you do it with the. Birds or fish that you get to end up with a four-dimensional base. They can, for instance, make a distinction between a mixture of blue and yellow and a green.
Why we can't make that distinction in our perceptual space. So it's a kind of empirical finding that the human color space is three-dimensional. And it partly depends on what receptors we have. I mean, some animals have more color receptors than we have, and there is some kind of theory of how we give go from the three different receptors, color receptors to the color perception.
It's also the black and white, uh, receptors, of course. Uh, but the, we end up with this kind of complimentary color. So, so, uh, blue is opposite to orange and, and, and so on in our perception, we get this color circle, which is, which is odd. You ask for other examples and it. That easy for me to give examples, [00:23:00] but on, if you talk about sounds, uh, we can talk about harmony space and harmony is, is very interesting because that depends on patterns between the frequencies.
So you get the kind of th things, some certain things or ho harmonious if the, if the frequencies match in, in mul multiple, so to speak. I mean, in Octa is double the frequency and, and, and, and, and so on. But the, they, they sound very similar. They are very similar, I mean, two, two terms that are distinguished by an octave.
They sound exactly similar, even if they are, uh, there is, um, certain, um, uh, certain distance in frequency. So there you also have that kind of of similarity doesn't fit with, with the, um, uh, herz, uh, representation of.
Benjamin James Kuper-Smith: It's funny that, um, I just mentioned sound as, as the counter example to color and. I did lots of music in my teenage years and know lots of music theory and all this kind of stuff. And it's funny that the one example I chose that I should have known about is the one that [00:24:00] is, doesn't actually fit either.
Um, yeah. But you're very right. Yeah, of course, of course not. An octave is, I mean, of course you, you, you do go up continuously, but then you do get these like weird jumps in there where suddenly things seem more similar than other things. Huh. But yeah, I mean, if you don't have an answer to this question, I can just take it out.
But like, why is it like one, it's just kind of, wouldn't it be more efficient to just code these things in a linear way every time? Like, uh, I'm just curious. It just, it's just seems like a really weird oddity that we have these dimensions that seem to exist as continuous variables, uh, in the outside world.
And then we, we structure it so differently in our mind. So I found it seems weird to me that some of the most basic dimensions seem to be coded in such a weird way, or is there like a real benefit to it? Like, yeah.
Peter Gardenfors: That's a very good question for color. I don't have any clue to why we end up with this kind of color [00:25:00] circle. What that helps us doing, uh, um, that must be some kind of ecological explanation for it. I mean, we talk about. Warm and cold colors. I mean the red and yellow or warm, and the green and blue or, or cold.
There is some kind of ecology to that. I mean, the, the warm things tend to be red and yellow and cold things tend to be blue and yellow, blue and, uh, green. Uh, and that could be some reason for why they're grouped together. Maybe there are other reasons for why we ended up with in, in a circle. Uh, it's a tough question, but, um, I guess there might be some explanations for, for, for that.
Um, uh, when it comes to sound, uh, think about how you recognize the vowel. The vowel is dependent on not on the frequency. I can say a high A and I can say a low A, uh, but it's the, the pattern between the overtones that determines that that's an A and not an O. So there there is more a pattern of frequencies rather than, rather than the [00:26:00] absolute frequencies to determine vows.
And how we identify vows. So, um, uh, I don't know if that's enough of a reason, but, um, it's the, it's the relations between the frequencies that are more important in, in, in a perception of sound than the, than the, uh, the absolute frequencies.
Benjamin James Kuper-Smith: Hmm. Okay. Yeah. Yeah. So I'm just trying to, I'm just trying to think about it, but I can't, I can't say anything intelligent to it. It's just, it's something I hadn't thought about, but now I realize that, uh, yeah, I, I'll probably think of something really smart to say, like tomorrow morning or something. Um, but yeah.
Yeah. The, the
Peter Gardenfors: the ER space is quite interesting. I, I had to look into it, so
Benjamin James Kuper-Smith: Yeah. Yeah. May, maybe I should, I should invite someone on to do, I mean, I, I, I have done some music episode, well, not, not really actually, but I want to do some music episodes in the future. Um, but yeah, but that's a, that's several conversation. Um, yeah, I mean, so to, to continue talking about dimensions a little bit, I mean, one question is of [00:27:00] course, um, oh, my question to me is like, what, which dimens.
Do you encode automatically? I mean, this maybe goes a little bit into neuroscience, um, and, uh, you know, as you said, it's maybe not your, your the strongest point, but, um, one thing I at least naturally wonder about is kind of, which dimensions do you encode at what time? And that kind of thing. Because in, in principle, you can, you can take every dimension you can think of and apply it to an object.
Sometimes that might not make sense, but you can still kind of try and do it or whatever. But is it, yeah. How do you kind of decide which dimensions to encode mentally or nearly? Is it just what's, whatever's relevant in the context or is there any, any more to it?
Peter Gardenfors: That's a very good question and quite complicated. I mean, William James said famously that the child, the newborn child, perceives the world as a blooming, buzzing confusion. So it's, it's just a lot of sensory in [00:28:00] input. And then the child has to make sense of this. And one of the first thing is to, uh, establish the spatial relations.
So we, we learn to pick up spatial structures quite early, and then we learn, of course, to coordinate the hand with the, with the hand movements, with our perception of the hands. We can direct our hands and, and, and, and so on. Uh, but that's the motor coordination. Um, but the child learns to separate more and more dimension.
And then one famous example is p hs example of, of conservation. He pours lemonade in, in, in a narrow glass, and then he pours it in a wide glass and he asks the child, which is the, which lemonade do you prefer? And the child always take the, the, the, the narrow gloss. But the, cause the lemonade looks higher.
So for the, for the. The hate of, of the, of the lemonade is the determining what is most. And it takes some time before it realizes that, that there is this vo dimension of volume that is con constant for, for a liquid. [00:29:00] So it has to add this volume, uh, into its representation of, of things in the world. So that's an dimension that you are definitely not born with, but you, we are, you learn by, via your experience with food and sand and water and, uh, lots of things that have volume that they sa, that the volume is very often conserved.
That's the con conservation, uh, principle. And then you, you use that dimension as a part. And then we, when we get to school, we learn about a lot of dimension from physics and uh, and, uh, chemistry and, and other things. We learn to, to perceive the world in, in, in new ways. There, there is no finite list of dimensions that we sort the world where we learn new things.
We learn social dimensions like, uh, hierarchies or, uh, kinship relations, uh, and, and things like that. We don't perceive them, but we have to learn them for social social relations. So in my book, I mainly use the perceptual dimensions because that's where we know something about the underlying [00:30:00] structure, but our thinking is full of different domains of thinking, different way.
We have different kinds of dimensions and for many of these we know nothing about how they are structured. Men mentally. Maybe status of hippocampus can help us here, but uh, that's for the future.
Benjamin James Kuper-Smith: Okay. Um, I have one question that kind of, I mean, so this is maybe a bit of a technical question, uh, but I, but I'm, I'm just genuinely curious because I don't know what the answer to this, uh, is. It's basically, uh, as always like reading your book and thinking about it and talking to about. I had this question of like, so I mean the, the, the, as you mentioned, one of the key parts of the theory of conceptual spaces is this idea of metrics and that you can calculate distances between them and, you know, you, you show that this can, you can have all sorts of, I mean we've, we've mainly talked about, uh, Euclid space implicitly, um, at least we've talked about that so far.
But you can have all sorts of different kinds of spaces. You can have, uh, like a graph there, a graph structure or all sorts of things. [00:31:00] One question I have is kind of. Can you, can you combine these or does it even make sense to calculate distances over different kind of metrics? So what I was thinking about, for example, like, let's say, I want to say, am I more similar to my older uncle or to my infant nephew?
You have these like two different dimensions, right? One is the, the continuous linear height and Oh, sorry. Age. Age. Um, and I guess you also have height difference, but, um, I was thinking of age and the other is you have this like family tree structure where, um, you know, I'm related to this degree, to that person or that person.
And it seems to me like I can ask that question and I can try and characterize some sort of distance in my head, but asking her more similar to, but it doesn't really make sense to, to calculate across those dimensions that much. Really. Um, I was just curious, like, is it, uh, yeah. Does that, does it work to like, you know, have a, one dimension is a graph and the other is a continuous one?
Or like Yeah. How does that.
Peter Gardenfors: Yeah, I [00:32:00] mean there are many concerts where, where you can combine different metrics of course, and then, then it's difficult to con to judge similarity. But in general, similarity is not, not something that is fixed, but similarity is very much dependent on, on, on the context. So, um, if, uh, if you are in the music context, then a piano is more similar to a flute than it is to an armchair.
But if you are in the, in the context of moving, uh, moving from one apartment to another one, then a piano is more similar to the armchair than to the flute. So, uh, the, the context depends. De de decides what are the relevant or most salient dimensions as I, I, as I called them. Um, and that will determine what, what is judged similar in, in, in, in, in, in particular situation.
So similarities is definitely context relative. Um,
Benjamin James Kuper-Smith: So an example I gave, for example, you would, one would say, okay, like, If I want to figure out who are more similar to what's, what you care about, like what's the relevant dimension here?[00:33:00]
Peter Gardenfors: Yeah, I mean if you, if you think about sharing clothes, then the height is much more similar than, and they're much more important than, uh, the kinship relations. But if you think about whom to invite to a party or to a wedding or whatever, then maybe kinship is, is the more, the more relevant, uh, uh, dimension here?
Benjamin James Kuper-Smith: Okay. Okay. Um, but would it work like mathematically to calculate distances across these different things or,
Peter Gardenfors: Uh, yeah. Yeah. I mean, if, if, if you have distances, I mean, in the graphs you don't have distances, but if you have distances, you can put weights on them. And it's just a matter of weight weighing the different, uh, domains. Um, so then you can change, uh, change the, um, the salience of the, of the dimensions. But in general, I mean, combining metrics, spaces with graphs is, uh, there, I don't have a clear answer to you.
Benjamin James Kuper-Smith: okay. Yeah. Yeah. Mm
Peter Gardenfors: I, I could maybe say something about the, the metrics because, and most people [00:34:00] think about spaces as ucli spaces, uh, but it turns out that, uh, that's not obvious when you look at how we perceive things. And if you take the color, color space, then we need to actually already there a polo coordinate, because it's a circle.
And we are, we have to look at the, the similarity is determined by the angle. It's not by the absolute, uh, Euclid distance. So for describing the color space, there is one polo dimension, and then there is this orthogonal, uh, dimension from, from black to white. So it's a combination there. Maybe you could do it as a sphere.
I mean, that would be another way of representing colors. And then you would've total, uh, polar coordinates. I don't know, which is empirically the best, uh, way to do it. But since I wrote a book, I've, I've been working, uh, on different aspects of semantics and. And, uh, I worked, uh, wrote a paper with a Dutch, um, linguist, uh, yourwas on prepositions, and it turned out in order to understand things like in front of, um, to the [00:35:00] left of an, an above and so on, it's much better to use polar coordinates than to use Euclid ones.
So we actually use po polo thinking for, for, uh, for, uh, our understanding prepositions. Uh, so it's not obvious that the Euclid space is the, the most natural way of, of how we think.
Benjamin James Kuper-Smith: Yeah, I found that aspect really interesting. And, um, yeah, I mean, one, one question I kind of had there was whether, I dunno whether this is exactly a criticism of, of it or not, but basically one question I kind of had is like, it seemed to me like it's, it's kind of difficult to falsify, um, or to find evidence against your theory in the sense that you can always kind of argue like, well, you're using the wrong metric or the wrong kind of space, you're using the wrong, uh, distance calculation or whatever.
Um, is, I mean, is this something you've, you've thought about much or
Peter Gardenfors: I, I, I thought that, I thought about it, but it gets, it's a kind of difficult problem cause it takes a lot of empirical [00:36:00] investigations. I mean, that's why I use the color space because it's fairly well established, but still people are fighting about whether, um, uh, the rrgb or the, uh, NNC s system is the best representation of, of c perception.
And they have slightly different geometry. All, all of them have three dimensions that, that they have in common. And, uh, I, I just picked the color spin as a, as a simple example of representing the, uh, the colors. But you can't falsify it because. If you'd really do hard work on people's similarity judgements, I mean, how, how do they judge similarity between colors?
Then you can make the distinctions between, between these spaces. But so far, I mean they, they, they are, there are very small differences. So there, there is a best empirical explanation, and I think my case for prepositions is actually easier because prepositions carve out quite, quite nice areas of the space.
Uh, I mean, being in front of is just, uh, yeah, particular area of space being behind and so on to the [00:37:00] left of, and, and these carvings out or done more or less and, and going around. And, uh, we, we have a lot of, lot of prepositions that depend on these polar coordinates. So the explanatory power of using polar coordinates is much larger for, uh, prepositions than it is to use lydian, uh, space to explain the meaning of prepositions.
It's a, well, it's a kind of indirect argument, but still it supports that the polar coordinates would be the, the natural, uh, representation of space.
Benjamin James Kuper-Smith: Of some spaces. Of all of them.
Peter Gardenfors: Your sound spaces. Yeah. But, okay.
Benjamin James Kuper-Smith: Yeah. By the way, just one thing I noticed, I guess I can tell that you are on Sweden is a bit further north because it's already a lot dark for you and for me it's still, I just realized that we started off roughly the same and it's changed like within an hour.
Peter Gardenfors: yeah, yeah.
Benjamin James Kuper-Smith: Um, Yeah, I mean, to some extent. Um, one thing I also wondered when I talked about falsifying is that it seemed to me that to some extent, that the point of your book is more to provide a framework through which you can kind of view all [00:38:00] of these things rather than a concrete, very specific testable theory that it's like super precise in that sense.
Peter Gardenfors: No, I, I depend on a lot of psychological work here. I mean, in order to establish how our perceptual spaces really look like him, and, and, and maybe, I mean, work on hippocampus can be, be a way into that because if we know the code and hippocampus, we can then maybe infer something about how we perceive things.
I mean, that might be fairly strong correlation between that. And we know that the cardinal space is quite good in, in the hippocampus, so, yeah.
Benjamin James Kuper-Smith: yeah. Um, I guess we've already talked a little bit about, um, I mean, you just mentioned literally the, your new work on semantics and that kinda stuff, and you published an entire book in 2014 called Geometry of Meaning semantics based on conceptual spaces. Uh, as I mentioned earlier, I know nothing about semantics.
So maybe, uh, this is something where I can, as I said, learn, learn probably the most from you. Uh, cause [00:39:00] there's, yeah, it's, it's a blank slate right now. You can just paint whatever you want onto it. Um, I was curious. What, I don't, I, I think you probably mentioned this in the book. Um, I don't think that I just came up with this, um, but it's, um, I, I can't remember.
I think it's in the semantics chapter. Um, basically the, the relationship between aspects or how different semantic concepts fit onto different parts of your theory. So for example, that adjectives are basically the quality dimensions. So if something is, uh, you. I mean, I guess red is maybe not colors, maybe not the best example here, but if someone, if, if someone is a nice person, then you can think of that as a continuous dimension and you know, it's one of the quality dimensions.
Um, is it then, is it, am I correct then in assuming that nouns, um, if you want to think of that, that way, are basically these prototypes in this space?
Peter Gardenfors: Well, that's exactly what I do in, in this book, the geometer, meaning that I, I want to explain why we have different word classes. I mean, [00:40:00] the main word classes are non adjectives, verbs, and prepositions. Uh, uh, there are lots of, not lost, but a few other classes, but these are the main ones. And, and, um, uh, if, if you study logic, computer science, then everything is a predicate and you don't make a distinction there.
So why do we have world classes? Well, they represent different kinds of things, and as you say, Addicts represents reading of some single space. And that's, uh, I mean the, the term red only concerns the color space. It doesn't concern time or shape or anything like that. So I put forward as a hypothesis that all additives only refer to single, uh, conceptual space or a single domain.
And, uh, of course that depends on having, being able to identify domains. So it's a, uh, it's a difficult hypothesis. And then nouns are combinations of properties from lots of domains. So a dog, dog has a size and a shape and a smell and a sound and, and a weight and a temperature, and a sha uh, uh, lots of, lots of aspects.
So nouns are [00:41:00] characterized by having lots of properties and correlations between properties. And then I did some work on prepositions and prepositions of basically spatial relations. But there are some, some. Prepositions that depend on force. For instance, for example, being on something is dependent on force or being against, leaning against something is dependent on forces.
So not only the spatial dimensions, but also others. And then I did a lot of work and I'm still working on verbs and there are two kinds of verbs. Uh, one. Uh, describing how you do something. They're called man verbs. Am I hitting or kicking or, or licking? I mean, I'm, I'm performing an action. And then I describe actions as, as patterns of forces.
That's my, my analysis. I use the force dimension to analyze manner verbs. And then there are result vers that describe what happens. Something gets heated, something is moved, something gets painted, and so on. There is a change of [00:42:00] property from being not red to red if you're painted, painting it red or from being cold, cold to war hot if you're heating a soup and, and, and so on.
And so I distinguish, I used the concept of spaces and different structures on the conceptor basis to distinguish between different, um, uh, different world classes. So that's one of the main themes in, in, in this book on, on the geometer.
Benjamin James Kuper-Smith: Okay. Yeah, I was wondering about, I was just, as I said, like, I mean, I've, I've read the Conceptual Spaces book, but not the one on, uh, semantics. And I was, yeah, I was really wondering, like, um, I, as, I can't remember whether you mentioned this in this, in the Conceptual Spaces book, but I was really thinking about verbs because I was like, okay, it's not like for, for, it seemed to be for nouns and additives, it's a lot clearer what they would be.
Um, but for verbs, I was like, I'm not entirely sure. And then, uh, I was just curious, like, because the, the, the like immediate answer I came with, is that a verb? A change in space, which I think corresponds roughly to some of the ones you said.
Peter Gardenfors: the result. Verbs, yes. I mean in, in, [00:43:00] in, in cons, in conceptual spaces. I didn't say very much about verbs at all, but I, that's an area where I worked quite a lot since, since then.
Benjamin James Kuper-Smith: Mm. Are there any verbs that don't fit into those two? Those are the two
Peter Gardenfors: Um,
Benjamin James Kuper-Smith: Oh, we don't talk about those.
Peter Gardenfors: There are some abstract verbs that are difficult to handle. I mean,
Benjamin James Kuper-Smith: Like hypothesize or what?
Peter Gardenfors: Yeah, exactly. Yes. We speculate. What is that?
Benjamin James Kuper-Smith: Yeah. What is, yeah, so, so what do you do with those? You just kind of say that you can't, you can't catch them all, or,
Peter Gardenfors: I, I, I say I have no idea what is the underlying conceptual space, so I skipped them.
Benjamin James Kuper-Smith: Yeah. Okay. By the way, how does that, um, I mean, I guess if you talk about adjectives, nouns, and verbs, that should probably be similar between. Swedish and English or German, French or
Peter Gardenfors: Oh, yeah. Yeah.
Benjamin James Kuper-Smith: how does that, are there any like, uh, again, I'm not assuming you know, all the languages of the world, um, but are there any languages that, uh, don't even, aren't that [00:44:00] where you can't even classify words into those concepts? Or is that pretty universal or?
Peter Gardenfors: No, no, it's, it's not, I mean, there are some basic differences actually. And, and one of the cases I happen to learn a little bit about is Mandarin. I mean, standard Chinese, where people are claiming, some linguists are claiming that they don't make a distinction between adjectives and verbs. Uh, so they don't say the table is brown, but I say the table brown, so is browning.
Uh, but on the other hand, there are linguists to say that yes, we can make distinctions and so on. And then this distinction between the manner and result verse, that's very clear in, in, in Mandarin, uh, funny dis distinction is that in, in a. In the European language, we only have one verb per basic sentence.
So either you pick a man verb, I, i I hit you, or, or we pick a result verb you, you, you bleed. Uh, or we don't use both. We can have prepositional phrases saying something or adverbs during the other
Benjamin James Kuper-Smith: I
Peter Gardenfors: but in Chinese,
Benjamin James Kuper-Smith: I walk and
Peter Gardenfors: yeah, we can, we can, yeah, we can do that. [00:45:00] But that's, that's a combination. But in Chinese, you can have both man verb and results verb in the same sentence, which is a bit odd for us.
Benjamin James Kuper-Smith: I was gonna ask you for example, but I guess that doesn't work in English then.
Peter Gardenfors: No, I, uh, I, I, I, I I can't do that. No,
Benjamin James Kuper-Smith: Yeah, yeah. No, it's just a, you know, um, I guess it's one of those things where you just can't really provide good examples if we're talking in
Peter Gardenfors: Uh, I, I should have pre, I should have prepared this, but I, I could find
Benjamin James Kuper-Smith: Well, but I mean, also in English, I guess you wouldn't have it, right? So it's,
Peter Gardenfors: Yeah. Well, I, something like it, it would be something like, I hit you bleed.
Benjamin James Kuper-Smith: eh,
Peter Gardenfors: That's not a grammatical sentence in English, but it's, it is apparently something you can say in Mandarin.
Benjamin James Kuper-Smith: I mean, you can say, I hit you, you bleed, I hit com, you bleed. That would, yeah.
Peter Gardenfors: Yeah, that's, that's two sentences. That's two.
Benjamin James Kuper-Smith: Ah, okay. Okay. Fair enough. Yeah. Yeah. Okay. You're right. I'm, I'm separating two main clauses here. Um, I cheated. Yeah. Um, [00:46:00] yeah, I mean, I'm, I'm, I'm still trying to, it's funny, like, I guess when I try and think about questions about semantics, one thing I'm very much constrained by is my lack of knowledge here about what I could ask.
Um, I mean, it's really weird, like language is a thing that I, I always say is the most boring thing in the world, but whenever I talk about it, I, I tend to be quite interested. So I have this very weird disconnect between how I think about it and how I actually seem to act about it.
Peter Gardenfors: Now, I mean, one interesting question that I have followed a bit is how children learn language. I mean, what concept do you pick up first? Uh, and it turns out that I pick up nouns before addicts, which seems odd because nouns are more complicated. On the other hand, nouns contain much more information, and that's much more correlation between the dimensions and learning that something is red or big, means that you have to separate out these dimension from all these correlations.
So, uh, according to my theory, it's not a wonder that that children are, have a preference for, for understanding [00:47:00] or learning nouns to, to, uh, adjectives.
Benjamin James Kuper-Smith: you mean like basically if, yeah, like intuitively. You, you might think that you would learn, uh, the, the adjective red first because it's one, it's a dimension or a space of a dimension or whatever, or height, let's say that's easier. Uh, you, you learn height, uh,
Peter Gardenfors: Mm-hmm.
Benjamin James Kuper-Smith: which is a noun, not an adjective. Uh, you learn, you learn tall.
Let's use that now. I
Peter Gardenfors: Yeah. That, that's an
Benjamin James Kuper-Smith: I found that adjective. Yeah. Um, Because it's one dimension, it will be simpler. But you mean it's more, I mean, is it more that children just learn specific items to, to find a sound that corresponds
Peter Gardenfors: that they, they're very good at picking out these correlations between properties. So the, there, there are correlations between sounds and shapes of, of theca. I mean, you have sounds and shape and, uh, furness and, and, and all these things go together, hang together and these, these form and a very natural cluster.
But if you look at things that are red, I mean, there there are, there are, there are uh, red flowers. There are red, those shoes are [00:48:00] red fruits, there are red, uh, everything. And what, how do you, how do you understand that what is common to this is, is the color? I mean, that's a, a more advanced and more abstract thinking.
Benjamin James Kuper-Smith: I mean, is it that you develop these dimensions to be able to differentiate between different, almost
Peter Gardenfors: This is exactly, that's what happens in pss con con conservation tasks, that you learn to see the dimension of volume as a separate one. You learn to see the dimension of a color as a separate one from, from all the things that go together.
Benjamin James Kuper-Smith: Okay. I was just curious again, like thinking about like, okay, we have to do these different types of words and how well they fit into your theory. I mean, is that then also if, if something let's say doesn't fit in, is that then also, yeah, I mean, is it kind of you, you try and see how far your theory takes you and how far you can fit it in, and then you say, okay, it doesn't work in this context, so something else is needed or what you do with that when you.
Peter Gardenfors: Most, most of the problems I have is the, the [00:49:00] problems that we don't know the underlying spaces. So I, I don't know how to analyze, uh, what it is to speculate or what to hypothesize and so on. I mean, I don't know what these abstract spaces look like, so, but for, for, um, perceptual spaces, I think it works quite well.
I mean, I, I, it's, it's more like a research program. I mean, and it, and, and, and the good thing about it that if this, Uh, ideas are correct, then that would be explained a lot about how we learn, um, uh, words as, as a child, some things are easier to learn than than others. And, uh, if I can find a fairly nice fit between the order in which children learn words and how, how complicated they auto represent the co conceptual spaces, I would be very happy.
Benjamin James Kuper-Smith: Yeah. Uh, just outta curiosity, do you have a theory of what an article is? Like the, or an and, uh, I guess that's a particularly question because it's, I mean, so I'm only really familiar with. Germanic and Romans languages. I don't really know any [00:50:00] other, but one thing I have noticed that it seems like a lot of other languages, I think, for example, Turkish and I think maybe Chinese also, I can't remember.
They don't use articles as far as I can tell,
Peter Gardenfors: No, no, no. Lots of lots of the, um, slavi languages, for instance, don't use articles. Yeah, yeah. No, I, I happen to know that articles have been derived out of demonstratives. I mean, this and that, and here and there. I mean, these, uh, uh, pointing words, so to speak. Yeah. And, uh, and, um, there are we in, in English or in in Germanic languages, we don't have very many, uh, uh, demonstratives.
Basically these four I mentioned. I mean here, there, and so on some languages, I mean, in English we have the old word of yonder, which means far away. I mean, here, there in yonder, I mean, that's a trition. Many languages have lots of demonstratives. And I happen to have worked with a. Language from Croatia, uh, Croatian is extremely rich in, in, in, in demonstrates.
You can talk, talk about this color and that size and and so on in terms of, uh, demonstratives. [00:51:00] And, uh, in my opinion, that's a kind of compensation for not having, not having articles. You say, instead of saying the book, you say this book or that their book, I mean that book. You say their book and Yeah.
Something like that. Uh, so, uh, you can replace, uh, articles with, with demonstratives, uh, in, in, in, in, in communicative functions.
Benjamin James Kuper-Smith: Okay. I didn't actually know the word demonstrative. I learned something new today.
Peter Gardenfors: These are pointing, pointing words. I mean pointing in place space or in time or in, uh, yeah.
Benjamin James Kuper-Smith: Mm-hmm. Yeah, it was funny, like once, once, once you mentioned it, I was like, yeah, I guess this is a different class of, of Word. Um,
Peter Gardenfors: But they turned out to fit quite nicely in the conceptual spaces framework.
Benjamin James Kuper-Smith: okay.
Peter Gardenfors: again, with polar coordinates. But
Benjamin James Kuper-Smith: Yeah. Yeah. Um, yeah. Um, I'd like to ask a little bit, I dunno how much you can, uh, say about this, but one, one kind of, uh, question I [00:52:00] had or. Just a topic I was thinking about is the idea of how well these conceptual spaces and the whole three levels of representation, how that fits in an evolutionary context and once you apply it to different species, I mean, again, I know you're not an ecologist, anything like that, but, uh, one thing I was curious for example, is, uh, well I also saw you have this book called How Homo Becomes Sapiens on the Evolution of Thinking.
So I figured maybe might, there's something about this, um, again, I haven't read that, uh, book, so I dunno what it's exactly about, but thinking about this kind of evolutionary context makes me wonder like whether, um, you know, do all species have all three levels? Uh, I'm assuming not. I think symbolic seems what we'd say is predominantly human.
Uh, but maybe let's just start there. Like is, um, as, as a basic question, do you all. Species have, uh, all levels of representation. And if not, is it like a hierarchy that you need to have the lower, to have [00:53:00] the higher, or can you have one.
Peter Gardenfors: I mean if I, if I simplify a lot, I mean, this is, this is the hierarchy. You start with the, the lowest level where, I mean, simple organisms react to certain, certain triggers. I mean, you react to the amount of glucose in, in water if you're on a mobile and, and then you direct yourself in that. Um, and, and that way you don't need concept.
You just have to follow gradient or gradients of light, gradients of food, gradients of butterflies follow gradients of pheromones. So, uh, it's a, it's a very, uh, simple mechanism there. Then if you come to mammals and birds, they are definitely have concepts. They can categorize things in whether something is edible or non-edible.
Whe whether something is a predator or not predator, you learn that and. Only humans have a fully developed symbolic, uh, system of communication. There are some cases in animals. Uh, for instance, the, the vert monkeys have three different [00:54:00] symbols for, or three different sounds for three different kinds of predators, um, for eagle, for a leopard, and for Python.
And so they have, you can't really think of them as simples because they're, they're, they're too, too simple. But what we have learned is to have a system of communication where we have level label, I'm sorry. We have learned to have a system of communication where we have labels for things. Animals are warning Christ and have made in Christ and they have food, Christ and so on.
Different sounds for different, but we can label things. We can take our categories, the concept we form the readings, we, we develop in our, in our minds and put labels on them. And then we can use, uh, words, symbols, or signs if you like, to communicate these label labels and thereby, uh, share our inner, inner, in inner world.
So there, there is an evolutionary order. Yes.
Benjamin James Kuper-Smith: Yeah. So you, so you can't, you can't get a conceptual level without the sub conceptual level.
Peter Gardenfors: No, this is my, my claim. And then, uh, in the neural network, [00:55:00] uh, the community would, would, uh, protest. But anyway,
Benjamin James Kuper-Smith: yeah. Yeah. But I guess it is an interesting, I mean, it, it seems to me also to some extent that the, the, the conceptual is some sort of dimensionality reduction almost of the sub conceptual is Okay. Yeah. So it seems like. Yeah, you need the dimensions to have the reduced space of those dimensions. Um, it's funny, like whenever you, whenever I think about this particularly, like you have these three levels in hierarchy, I wonder like what would be the fourth level?
But I guess that's not something above symbolic is not something we can think about by definition, basically, or Yeah. Yeah. I mean, so your book was published in 2000, as you mentioned? Uh, so that's almost 25 years ago now. And I guess you also call it a research program, um, which is a fantastic word I'll use whenever I, I'm not, something's not exactly figured out yet.
Um, but um, yeah, I'm curious like kind of it's, yeah, it's been 25 years. We were only mentioned some of the grid sales stuff. [00:56:00] Um, but like, yeah. What are kind of some developments that happened in the last 25 years or something that you think might happen in the near.
Peter Gardenfors: Yeah. Now to my surprise, it's been applied to a lot of areas. Uh, uh, I was hoping some people would apply it in neuroscience, but it took 20 years before that took off. And, and, uh, now, now everybody is talking about spatial representations. I like that very much. Um, it, it's taken off a bit in robotics, uh, and, uh, ai and I may say something more about that, but there were other areas, uh, and um, and one area that surprised me quite a lot was in, uh, in, um, in the geosciences.
There was a group in, in, in minster in, in Germany who started using conceptual spaces to represent geographical concepts about land areas, land types and so on. And they did a really good work on that. So I, uh, that was total surprise.
Benjamin James Kuper-Smith: Yeah. How do they apply it? Do you know or,
Peter Gardenfors: Uh, I, I, I don't, I'm sorry I can't give you an example here, but, but they classif to [00:57:00] classify different types of land areas and, and, uh, and, uh, whether something is a march or a, a lake or a estu area or, uh, and so on. Yeah.
Benjamin James Kuper-Smith: Mm-hmm.
Peter Gardenfors: Uh, yeah, whether it's something is a mountain or a hill, I mean, that's a simple distinction, but, uh, yeah.
Yeah. Um, then. I wrote the book for philosophers and cognitive scientists, but it's been, uh, some people in robotics have, have started using the ideas, and I'm, I'm really happy about that because I think that if you rep stop using only symbolic programming and start doing things more in terms of vectors, I mean programming terms, uh, uh, concepts in terms of vectors, vector spaces and, and radis in spaces and so on.
It'll be much easier for a robot to learn a new concept or for an AI system to learn new concept. I mean, you have these big AI system based on deep learning and where you, where you pr train them on, on 100,000 different faces or, or, [00:58:00] or whatnot. And then they can recognize new faces. But if you. Some kind of dimensional, uh, representation of, of the concept.
Then I, I think that the learning process could be made much, much quicker in, in, uh, by using these kind of geometrical, uh, representations. And then of course, you can turn that into symbolic representation and, and, and have a new language for, for things. I mean, think about dropping a number of, of robots on a, on a distant planet.
They can't communicate with Earth. They have to find, look at everything new. I see. And they have to communicate. They have different sensors. They have, they have, uh, cameras and microphones and geer, ma ma and thermometers and, and and whatnot. And they have to build up some kind of concepts, uh, conceptual representation of what they're experiencing in the world.
And they have to communicate about that. I think that would be much quicker if you did it via some kind of of dimensional representations.
Benjamin James Kuper-Smith: Yeah, and I guess especially what you [00:59:00] mentioned, the, the, the, the prototypes and the distant metrics and all that kind of stuff, it seems to me that's, it's just a very convenient way of. In a way, like, one thing I found really fascinating is that it's just a very efficient way of storing information and, and the relationship between, uh, all sorts of different things, but yeah.
Yeah, yeah. Makes, I mean, I guess it's the whole like ai, neuroscience, psychology, uh, back and forth is this idea that if, if it's much more efficient for humans to learn that way, then it might also be more efficient and quicker for AI systems to learn that way. Yeah, and I guess, I guess also I'd imagine people in ai, for them it would be quite natural because, you know, you put it between the connectionist model that I suppose it's more of the deep learning new stuff and then the
Peter Gardenfors: It involves different programmer methodologies. I mean, you have standard programs for, for the symbolic level, and you have neural networks for this subs. Symbolic, developing this kind of vector computation and, and, um, oid Ations and whatnot is, is a different kind of programmer methodology, but [01:00:00] it can be done.
I mean, it's not, and there is a, it takes a different technique.
Benjamin James Kuper-Smith: but that hasn't been developed yet, or.
Peter Gardenfors: There are, there are attempts, there are some, uh, cases done. Yeah. But it's fairly small, so.
Benjamin James Kuper-Smith: Okay. Okay. Sounds exciting. Whatever's gonna, whatever's gonna come next. In this, uh, by the way, are you still, um, are you mainly working on the semantic aspects or what are you most in, like, personally, what are you most interested in?
Peter Gardenfors: I'm, I'm mainly working on the semantic aspect, but I also have a lot of contact with people in, in, uh, robotics and ai, and I'm discussing with it, and I'm trying to, uh, show them that, that the, these kind of models are, can be useful in, in, in AI robotics.
Benjamin James Kuper-Smith: mm-hmm. Um, I, I, I'm trying to have a few questions that I asked most. And that's kind of largely independent, although it can, obviously, you can make it completely relevant to what we talked about. Um, and obviously because I didn't send you these questions before, you can take as much time as you want and I'll edit it to [01:01:00] make it very nice and short.
Uh, well as if there's no pause and you immediately thought of it or I can take it out. One question, uh, just in general is like, what's something that, uh, you wish you learned sooner? It can be from academia or science or life, uh, whatever you want. Just some, I don't know. I guess everyone has, uh, some mistakes that repeated a few times.
Too many. Um, yeah. I'm curious if.
Peter Gardenfors: Since I became a cognitive science scientist via computer science and philosophy, I wish I had a better background in, in psychology and, uh, given a, a, a very long life, I would have included neuroscience in that too, but, uh, uh, that would have probably be too much for a young fellow to, to, to learn about all these things about psychology.
I mean, the, the psychological methods and so on is something I miss. I have a little bit of a background in linguistics and, uh, and [01:02:00] I've broadened that later. But, uh, still I'm not a linguist then, uh, from life. I mean, there are, I've had different kinds of hobbies. Uh, and, uh, if you want to have a really personal thing, I, I started with Judah when I was 35.
Uh, yes. Uh, and I went on, I really loved that sport and I ended when I was 55. Uh, but I wish I had started that much earlier. I thought it was so fun. It was so great, uh, to do, to do judo. So, uh, that's something I, I wish I had started much earlier with.
Benjamin James Kuper-Smith: Uh, why did you just stop?
Peter Gardenfors: I was 55. I, I stopped by taking my, the, the black belt and then my, when you take the black belt, you have to do this cut at this choreograph to do, to affairs, and you have to throw yourself and, and your opponent on the floor Hundreds of times you, you practice.
So, so my body was simply worn out.
Benjamin James Kuper-Smith: Okay. Yeah. Yeah. It's funny, I al I actually also tried to do, um, uh, some martial art, uh, present jujitsu, [01:03:00] which I guess is becoming a lot more popular in recent years. I stopped doing it also because I moved and then it was too far away from the gagen blow, blah, blah. But I, I think I got injured like twice within the first three months.
It was also, um, yeah, I guess that happens probably less if you start earlier with these kind of
Peter Gardenfors: Hmm, Hmm.
Benjamin James Kuper-Smith: Um, Yeah, maybe just briefly about, uh, the first point you mentioned about all these different disciplines and if you, you know, if you had time you'd learn all the different, you know, neuroscience, psychology kind of things.
As someone who very much is at the intersection of neuroscience, psychology and a bit of economics, it does often feel like it's a lot. Uh, so I'm curious, like how do you, uh, how do you deal with that? Because I guess one difficulty I have in general just kind of sounds like you have to learn everything and.
Peter Gardenfors: I, I deal with it by, by still being very curious and, and reading about a lot of different stuff. I mean, I've actually read quite a lot in economics as well, uh, in particular game theory and decis decision theory in mo in modern, uh, areas. Uh, uh, so I, I try to follow, I, I, I, I read a lot. I listen to a lot of [01:04:00] lectures and I go to seminars and I go to conferences.
Uh, so I, I still think of myself as having an open mind and being very curious about. I don't, I don't want to let get locked up in any particular small research question. I mean, I, I'd rather take wild blows at the, at the bigger area than, uh, than small and controlled movement movements in a small
Benjamin James Kuper-Smith: Ending up as your center in a four-legged split
Peter Gardenfors: Yeah, exactly. Yeah.
Benjamin James Kuper-Smith: that. Okay.
Peter Gardenfors: Yep. Yep.
Benjamin James Kuper-Smith: uh, the, the final question is, um, kind of what's, and what's an old paper or book that's been overlooked or that you think more people should read? Doesn't necessarily have to be old, but I think there's a lot of very good old papers that people.
Anymore. Um, I dunno if anything comes to mind.
Peter Gardenfors: There. I have to think th this book has been read, but David Morris' book on vision was, was for me, the prime example of how to do cognitive science. I mean, he, he had a good [01:05:00] background in neuroscience. He had a good background in, in co computing, and he developed very, very, um, good new models, a new, uh, in a very creative way.
I mean, that, that, that was for me, a one of the real big B breakthroughs in, in what can be called cognitive science. Uh, so I mean, that book is widely read, but I, I still, I, I think we shall not for, forget him because he was such a unique person in, in, uh, in creating a new area of, of, of, of research. Yeah.
So that, for me, that's one of the prime examples in within the cognitive science.
Benjamin James Kuper-Smith: Yeah, that's actually a great example because, um, especially, you know, I, as a, as I said before we're recording, I, I did my masters in kind of cognitive competition neuroscience, and there it feels like every lecture started with David Ma. Um, because it's, you know, always at three levels and I think it's a great way of organizing it.
Um, But I haven't actually read it. I haven't read it. Yeah. I've heard it so often that I feel like I know it, but I haven't actually. I mean, you know, also not [01:06:00] exactly doing that, but it's, um, I think this is the perfect
Peter Gardenfors: read it because you should read it becau, in order to follow his, how he builds up his argument. And it is, it's very logical. Okay. In, in retrospect, some of his ideas have been rejected, but his way of, of building up the story is, is just amazing. It's, it's really created really, really strict and, and, and well done.
Yeah. I I was very impressed by that book. Yeah.
Benjamin James Kuper-Smith: Okay. Well,
Peter Gardenfors: Yeah. So go ahead and read it.
Benjamin James Kuper-Smith: I'll do that. Okay.